Re: Defuzzification/Information loss

Ibrahim Larchie (larchiei@tuns.ca)
Fri, 26 Jan 1996 14:32:11 +0100


Defuzzification with the centroid algorithm although popular is quite
dissipative in terms of information conservation. Remember that
that it essentially is a 'smoothing ' method based on the central
limit theory. If your number(s) distribution is skewered in any fashion
( and this property is important) then it is probably not the method
of choice.

To test the efficacy method with a system characterized by input-output
data and a fuzzy relation : G --> G(X,Y,R) a simple way is to compare
the the values obtained by the defuzzification process with the observed
values: e.g. divide Y in 2 segements form the normalized statistic say

M = K*(Yo -Yd)

where Yd is defuzzified values expected after using Yo to build the
model.

Of course to minimize the overall error, then use a suitable adaptive
algorithm to reduce a performance index which optimizes R in the above

A good reference for further information is perhaps some of the
early papers of Prof.L-X Wang et al.
for non-robust algorithm try:Ying-Chin Lee, Chyi Hwang et al in
" A combined Approach to Fuzzy Model Identification" IEEE Trans
on sys.Man and Cyb. May 1994.

For the merits and demerits of Defuzz methods and some
exotic ones try Yager(PhD. thesis. 1994 or some of his Pubs)

I hope this helps

Ibrahim Larchie
==========================================================
1) larchiei@newton.ccs.tuns.ca 2) Physiol. Modllg Lab
larchiei@ac.dal.ca Dept. of Elect. Eng.
Ilarchie@biophy.bp.dal.ca Technical Univ. of Nova Scotia
PO BOx 1000, Halifax NS B3J 2X4
Fax:(902)4207551 Tel: (902)420-7721
Website:http://www.tuns.ca/~larchiei/
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"...Evolution cannot beat poor engineering

>
> I am working on a problem which requires defuzification of the fuzzy
> number(s) which I modelled. They are trapezoidal (sometimes Triangular) in
> nature. Does anyone know of some references on INFORMATION LOSS after
> defuzzification. I would like to find out how much information I lose if
> I proceed with my defuzzification. I intend to use the centroid method.
>
> Thank you
> Maxwell
>
>